In the modern hydraulic servo system, the servo valve is the core component to control the movement of the actuator, and its dynamic response characteristics directly affect the control accuracy and stability of the system. In order to improve the response speed and tracking performance of servo system, feedforward compensation technology is often used. This paper will discuss the basic principle and calculation method of servo valve feedforward compensation.
First, the basic concepts of servo valve and feedforward compensation
Servo valve is a device that can accurately control the flow and direction of hydraulic oil according to the input electrical signal, and is widely used in high-precision motion control systems. However, the dynamic performance of the system will be limited because of the response delay and nonlinear characteristics of the servo valve.
Feedforward compensation is a control strategy based on system model. By predicting the expected output of the system and applying the corresponding control quantity in advance, the dynamic lag of the controlled object is offset, thus improving the response speed and tracking accuracy of the system. In the application of servo valve, feedforward compensation is usually combined with feedback control (such as PID) to achieve better comprehensive control effect.
Second, the mathematical model of servo valve feedforward compensation
Assume that the dynamic characteristics of the servo valve can be expressed by a second-order transfer function:
$$ G_v(s) = frac{K_v}{s^2 + 2zetaomega_n s + omega_n^2} $$
Among them:
-$ K_v $: servo valve gain;
-$ zeta $: damping ratio;
-$ omega_n $: undamped natural frequency.
If we want the system to respond quickly to a certain expected input $ r(t) $,we can design a feedforward controller $ G_{ff}(s) $ to compensate the phase lag and amplitude attenuation of the servo valve. Ideally, the feedforward compensator should be the inverse of the transfer function of the servo valve:
$$ G_{ff}(s) = frac{1}{G_v(s)} = frac{s^2 + 2zetaomega_n s + omega_n^2}{K_v} $$
Third, the realization and calculation steps of feedforward compensation
1. Establish the servo valve model.
Firstly, the dynamic model of the servo valve is established through experiments or parameters provided by manufacturers, and its key parameters, $ K_v, zeta, omega_n $,are identified.
2. Design feedforward controller.
A feedforward controller is designed according to the above transfer function. Considering that the high frequency noise may be amplified in the actual system, a low-pass filter can be added to the feedforward controller or the high frequency band can be limited.
3. Combined with feedback control
Feedforward control can’t replace feedback control because it can’t cope with the disturbance and modeling error in the system. Therefore, the output of feedforward compensation is usually added with the output of feedback controller (such as PID) as the final control signal of servo valve:
$$ u(t) = u_{ff}(t) + u_{fb}(t) $$
4. Simulation and verification
Before practical application, the system is modeled and simulated by simulation tools (such as MATLAB/Simulink) to verify the effect of feedforward compensation, and the controller parameters are adjusted according to the simulation results.
Fourth, the application example analysis
In an electro-hydraulic servo position control system, the rise time of the system is shortened from 0.3 seconds to 0.15 seconds, and the overshoot is reduced by 10%, which significantly improves the dynamic response performance and tracking accuracy of the system. This shows that a reasonably designed feedforward compensation can effectively improve the control quality of the servo system.
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To sum up, feedforward compensation of servo valve is an important means to improve the response speed and accuracy of hydraulic servo system. The dynamic performance of the system can be effectively improved by establishing the mathematical model of the servo valve, designing a suitable feedforward controller and combining it with feedback control. In the future, with the development of control theory and modeling technology, feedforward compensation will play an important role in a wider range of engineering fields.